value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Curvature, steps to trace the cartesian curve

steps to trace the cartesian curve

Polygon on a coordinate, a square tile measures 12 inches by 12 inches each...

a square tile measures 12 inches by 12 inches each unit on a coordinate grid represents 1 inch (1,1) and (1,13) are two of the coordinate of the tile drawn on the grid what are the

Sqrt n- sqrt 8836, How many integers satisfy (sqrt n- sqrt 8836)^2 Solutio...

How many integers satisfy (sqrt n- sqrt 8836)^2 Solution) sqrt 8836 = 94 , let sqrt n=x the equation becomes... (x-94)^2 (x-94)^2 - 1 (x-95)(x-93) hence  93 8649  the number o

Example of quadratic polynomial, Factor following.                    x ...

Factor following.                    x 2 - 20 x + 100 Solution In this case we've got three terms & it's a quadratic polynomial.  Notice down as well that the constant

Speed and distance, Two trains were traveling in opposite directions, movin...

Two trains were traveling in opposite directions, moving away from one another. One train was moving at 5 miles per hour. The other train was moving at 6 miles per hour. They were

How to solve two-step equations, How to solve Two-Step Equations? Two-s...

How to solve Two-Step Equations? Two-step equations involve two math operations - one operation is addition or subtraction. The second operation is multiplication or division.

what fill amount are they searching, Brewery has 12 oz bottle filling mach...

Brewery has 12 oz bottle filling machines.  Amount poured by machine is normal distribution mean 12.39 oz  SD 0.04 oz. Company is interested in in reducing the amount of extra beer

Course work2 , (b) The arity of an operator in propositional logic is the n...

(b) The arity of an operator in propositional logic is the number of propositional variables that it acts on – for example, binary operations (e.g, AND, OR, XOR…) act on two propo

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd